Hyperreflexivity of the space of module homomorphisms between non-commutative Lp-spaces

Abstract

Let M be a von Neumann algebra, and let 0<p,q≤∞. Then the space HomM(Lp(M),Lq(M)) of all right M-module homomorphisms from Lp(M) to Lq(M) is a reflexive subspace of the space of all continuous linear maps from Lp(M) to Lq(M). Further, the space HomM(Lp(M),Lq(M)) is hyperreflexive in each of the following cases: (i) 1≤q<p≤∞; (ii) 1≤p,q≤∞ and M is injective, in which case the hyperreflexivity constant is at most 8.